This paper aims to serve as a comprehensive guide for researchers and practitioners, offering insights into the current state, potential applications, and future research directions for generative artificial intelligence and foundation models within the context of intelligent vehicles. As the automotive industry progressively integrates AI, generative artificial intelligence technologies hold the potential to revolutionize user interactions, delivering more immersive, intuitive, and personalised in-car experiences. We provide an overview of current applications of generative artificial intelligence in the automotive domain, emphasizing speech, audio, vision, and multimodal interactions. We subsequently outline critical future research areas, including domain adaptability, alignment, multimodal integration and others, as well as, address the challenges and risks associated with ethics. By fostering collaboration and addressing these research areas, generative artificial intelligence can unlock its full potential, transforming the driving experience and shaping the future of intelligent vehicles.